In this paper, it is proved that the small deformation strain tensor can be
used instead the fundamental metric tensor of the GeneralTheoryofRelativity,
in order to formulate a DynamicTheoryofGravitation. Also, a solution
of the velocity of the gravitational interactions is given in terms of the escape
velocity due to the apparent size of the heavenly bodies. This last paragraph is
the motivation and the importance of the study here presented. Thus, when it has
a couple of celestial bodies separated by a distance in space, its apparent sizes
as seemed at a distance play a special role in the gravitational interactions. This
is so because of some effect over the size due to the very big distance in space.
In that situation, the values of their escape velocities are dependent on their
mass, and critically on their apparent radius. It is proved that they are the medium
used by the gravity to transmit its effects like propagating force of nature. Then,
when the escape velocities meet in some point of the space between the bodies, they
pull each other; because they are the carriers of the respective attractive gravitational
fields. In other words, the escape velocity due to the apparent size is the exchanging
coin in the gravitational interactions. Also it is proposed that such a dynamic
process is the responsible for the strong link which is established between any
couple of interacting heavenly objects in the Universe.

Fierros, A.
(2006) The Hamilton-Type Principle in Fluid Dynamics. Fundamentals and Applications
to Magnetohydrodynamics, Thermodynamics, and Astrophysics. Springer-Verlag, Wien.